Question

please solve this all problems with process please​

Answer 1

Let us assume that √2 is a rational number.

So, √2= a / b (a and b are co prime i.e. no common factor other than 1)

=> √2b = a

squaring both sides

(√2b)²= a²

=> 2b² = a²

As 2 divides a² ,it will also divide a.

Now, let a = 2c (where c is some integer)

We know that,

a² = 2b²

putting a = 2c in above equation

(2c)²=2b²

4c²=2b²

2c²=b²

Hence, 2 divides b², it will also divide b.

So, 2 is a factor of a and b both as 2 divides a and b.

But we have assumed that they are co prime and cannot have any common factor other than 1.

This contradicts our assumption.

Hence, our assumption is wrong.

√2 is irrational number.

By using exactly same method you can solve the other parts.

P.S. Please mark as brainliest.